Timpanogos cave is well worth your time. The pictures really don't do it justice. The hike is 1.5 miles up a steep, but paved trail. A ranger takes you through the cave for about an hour with an average temperature in the cave of about 46 degrees. Then it's a steep downhill hike back down the mountain that will make your knees not very happy. But, the caves are worth all of that. Inside the cave is amazing. I'm pretty much a claustrophobic person, but I did pretty good in the cave. Stalactites and stalagmites, large open rooms in the caves to tiny walkways. Really cool. I want to take my wife back up there, but I don't think my 2 yr old is ready for that sort of thing yet!
If you do go this summer take this one suggestion. Go early. The first tour through the cave starts at 9:00 am and there were only about 10 people in our tour. It took us about an hour and a half to hike to the cave, although we had some children with us, but plan to park by about 7:30 am. I know that's early, but it will be worth it to you because the tour will have less people and the trail wont be as crowded. When we were on our way down at about 10:00, there were a ton of people on their way up. Take that suggestion for what it's worth and enjoy the caves!